Animate clouds texture for blender sky
That really depends on the node setup. If you go to this tutorial and follow along with what it has to say, then there are specific drivers in the tutorial that will allow your clouds to move and be very flexible.

Here's the .blend file in which you can append from! Just make sure your project is in Cycles, and press Shift + F1 (append) and go to path\suppliedblend.blend\world\sky.
;)



EDIT:

Here are some further steps on how to animate the clouds without actually having to watch the tutorial. Now, when going to edit this answer, I realized that my supplied .blend file wasn't actually optimized to have these animate-able  properties. So, It's really quite simple to add that feature. Make an edit to the provided node setup and add a new node (Shift+A) and add a mapping node. (Vector>>Mapping) Put your node in between your Texture Coordinates node, and your Noise Texture node. That way, the mapping node will have the output of the texture coordinates node going into the input of the mapping node. It's output will then go into the input of the noise texture node. Simple. Once this has been added, to make your clouds move you just need to keyframe the location coordinates parameters. If you hover over one of the sliders and press I then you will have keyframed your value. Make sure that the other keyframe is far enough away from the first to achieve a realistic effect.